TY  - JOUR
A1  - Ripoll, Jean-François
A1  - Loridan, Vivien
A1  - Cunningham, G. S.
A1  - Reeves, Geoffrey D.
A1  - Shprits, Yuri Y.
T1  - On the time needed to reach an equilibrium structure of the radiation belts
JF  - Journal of geophysical research : Space physics
N2  - In this study, we complement the notion of equilibrium states of the radiation belts with a discussion on the dynamics and time needed to reach equilibrium. We solve for the equilibrium states obtained using 1-D radial diffusion with recently developed hiss and chorus lifetimes at constant values of Kp = 1, 3, and 6. We find that the equilibrium states at moderately low Kp, when plotted versus L shell (L) and energy (E), display the same interesting S shape for the inner edge of the outer belt as recently observed by the Van Allen Probes. The S shape is also produced as the radiation belts dynamically evolve toward the equilibrium state when initialized to simulate the buildup after a massive dropout or to simulate loss due to outward diffusion from a saturated state. Physically, this shape, intimately linked with the slot structure, is due to the dependence of electron loss rate (originating from wave-particle interactions) on both energy and L shell. Equilibrium electron flux profiles are governed by the Biot number (tau(Diffusion)/tau(loss)), with large Biot number corresponding to low fluxes and low Biot number to large fluxes. The time it takes for the flux at a specific (L, E) to reach the value associated with the equilibrium state, starting from these different initial states, is governed by the initial state of the belts, the property of the dynamics (diffusion coefficients), and the size of the domain of computation. Its structure shows a rather complex scissor form in the (L, E) plane. The equilibrium value (phase space density or flux) is practically reachable only for selected regions in (L, E) and geomagnetic activity. Convergence to equilibrium requires hundreds of days in the inner belt for E>300 keV and moderate Kp (<= 3). It takes less time to reach equilibrium during disturbed geomagnetic conditions (Kp = 3), when the system evolves faster. Restricting our interest to the slot region, below L = 4, we find that only small regions in (L, E) space can reach the equilibrium value: E similar to [200, 300] keV for L= [3.7, 4] at Kp= 1, E similar to[0.6, 1] MeV for L = [3, 4] at Kp = 3, and E similar to 300 keV for L = [3.5, 4] at Kp = 6 assuming no new incoming electrons.
Y1  - 2016
U6  - https://doi.org/10.1002/2015JA022207
SN  - 2169-9380
SN  - 2169-9402
VL  - 121
SP  - 7684
EP  - 7698
PB  - American Geophysical Union
CY  - Washington
ER  -